Group #22608022 — subgroups

Subgroups — #22608022

Order 9344.

152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11924003	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556525	C₂	1	1	yes	maximal, characteristic
3	C₂×#107×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₇₃	—	2	1	no	—
5	C₂×#11924003	—	2	1	no	—
6	C₂×#11924003	—	2	1	no	—
7	C₂×#11924003	C₄	1	2	yes	complemented
8	#14556525	—	2	1	no	—
9	#14556525	C₄	1	2	yes	complemented
10	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
12	#107×C₇₃	—	2	1	no	—
13	#107×C₇₃	C₄	1	2	yes	complemented
14	C₂²×Dic₇₃	—	4	1	no	—
15	C₄⋊Dic₇₃	—	2	2	no	—
16	C₄⋊Dic₇₃	—	4	1	no	—
17	#11924003	—	2	2	no	—
18	C₂²×C₄×C₇₃	—	4	1	no	—
19	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
26	C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₄⋊C₄×C₇₃	—	4	1	no	—
28	C₂³×C₇₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	4	2	no	—
30	C₂×C₄×C₇₃	—	8	1	no	—
31	C₂×C₄×C₇₃	—	8	1	no	—
32	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
36	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₃	Q₁₆	1	1	yes	characteristic
38	C₂×Dic₇₃	—	4	2	no	—
39	C₂×Dic₇₃	—	8	1	no	—
40	C₂×Dic₇₃	—	8	1	no	—
41	C₈×C₇₃	C₄²	1	1	yes	characteristic
42	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
44	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₇₃	#102	1	1	yes	characteristic
46	C₂²×C₇₃	#102	1	1	yes	characteristic
47	C₂²×C₇₃	#107	1	1	yes	characteristic
48	C₂²×C₇₃	D₁₆	1	1	yes	characteristic
49	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
50	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
51	C₂²×C₇₃	Q₃₂	1	1	yes	characteristic
52	C₄×C₇₃	—	8	2	no	—
53	C₄×C₇₃	#95	1	1	yes	characteristic
54	C₄×C₇₃	#103	1	1	yes	characteristic
55	C₄×C₇₃	#103	1	1	yes	characteristic
56	C₄×C₇₃	#106	1	1	yes	characteristic
57	Dic₇₃	—	8	2	no	—
58	C₂×C₇₃	#340	1	1	yes	characteristic
59	C₂×C₇₃	#357	1	1	yes	characteristic
60	C₂×C₇₃	#357	1	1	yes	characteristic
61	C₂×C₇₃	#358	1	1	yes	characteristic
62	C₂×C₇₃	#358	1	1	yes	characteristic
63	C₂×C₇₃	#366	1	1	yes	characteristic
64	C₂×C₇₃	#367	1	1	yes	characteristic
65	#1380	—	73	1	no	maximal, Sylow
66	C₇₃	#1380	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₁₆	—	73	1	no	—
68	C₂×#107	—	73	1	no	—
69	C₂×#107	D₇₃	1	1	yes	characteristic
70	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
71	C₂×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄⋊C₄	—	146	1	no	—
73	C₂×C₁₆	—	73	2	no	—
74	C₂×C₁₆	—	146	1	no	—
75	C₂×C₁₆	—	146	1	no	—
76	#107	—	2	1	no	—
77	#107	—	73	2	no	—
78	#107	—	146	1	no	—
79	#107	Dic₇₃	1	2	yes	complemented
80	C₂²×C₄	—	4	1	no	—
81	C₂²×C₄	—	292	1	no	—
82	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
83	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
84	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
85	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
86	C₂×C₈	D₂₉₂	1	1	yes	characteristic
87	C₂×C₈	C₂×Dic₇₃	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	4	1	no	—
91	C₄⋊C₄	—	292	1	no	—
92	C₄⋊C₄	—	146	2	no	—
93	C₁₆	—	146	2	no	—
94	C₂³	#11924013	1	1	yes	characteristic
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	—	8	1	no	—
97	C₂×C₄	—	8	1	no	—
98	C₂×C₄	—	292	2	no	—
99	C₂×C₄	—	584	1	no	—
100	C₂×C₄	—	584	1	no	—
101	C₂×C₄	#11924005	1	1	yes	characteristic
102	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
103	C₂×C₄	#11924007	1	1	yes	characteristic
104	C₂×C₄	#11924015	1	1	yes	characteristic
105	C₂×C₄	#11924016	1	1	yes	characteristic
106	C₂×C₄	#11924018	1	1	yes	characteristic
107	C₈	C₄×Dic₇₃	1	1	yes	characteristic
108	C₈	#11924005	1	1	yes	characteristic
109	C₈	#11924007	1	1	yes	characteristic
110	C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
111	C₂²	#14556511	1	1	yes	characteristic
112	C₂²	#14556512	1	1	yes	characteristic
113	C₂²	#14556524	1	1	yes	characteristic
114	C₂²	#14556532	1	1	yes	characteristic
115	C₂²	#14556534	1	1	yes	characteristic
116	C₂²	#14556535	1	1	yes	characteristic
117	C₂²	#14556537	1	1	yes	characteristic
118	C₄	—	8	2	no	—
119	C₄	—	584	2	no	—
120	C₄	#14556498	1	1	yes	characteristic
121	C₄	#14556514	1	1	yes	characteristic
122	C₄	#14556515	1	1	yes	characteristic
123	C₄	#14556522	1	1	yes	characteristic
124	C₂	#17988349	1	1	yes	characteristic
125	C₂	#17988387	1	1	yes	characteristic
126	C₂	#17988388	1	1	yes	characteristic
127	C₂	#17988390	1	1	yes	characteristic
128	C₂	#17988391	1	1	yes	characteristic
129	C₂	#17988412	1	1	yes	characteristic
130	C₂	#17988414	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924003

C₂

yes

maximal, characteristic

C₂×#14556525

C₂

yes

maximal, characteristic

C₂×#107×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₃

—

C₂×#11924003

—

C₂×#11924003

—

C₂×#11924003

C₄

yes

complemented

#14556525

—

#14556525

C₄

yes

complemented

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

#107×C₇₃

—

#107×C₇₃

C₄

yes

complemented

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

Q₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

D₁₆

yes

characteristic

C₂²×C₇₃

SD₃₂

yes

characteristic

C₂²×C₇₃

SD₃₂

yes

characteristic

C₂²×C₇₃

Q₃₂

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×#107

—

C₂×#107

D₇₃

yes

characteristic

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

#107

—

#107

—

#107

—

146

—

#107

Dic₇₃

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂×Dic₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₁₆

—

146

—

C₂³

#11924013

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

100

C₂×C₄

—

584

—

101

C₂×C₄

#11924005

yes

characteristic

102

C₂×C₄

C₂²⋊Dic₇₃

yes

characteristic

103

C₂×C₄

#11924007

yes

characteristic

104

C₂×C₄

#11924015

yes

characteristic

105

C₂×C₄

#11924016

yes

characteristic

106

C₂×C₄

#11924018

yes

characteristic

107

C₈

C₄×Dic₇₃

yes

characteristic

108

C₈

#11924005

yes

characteristic

109

C₈

#11924007

yes

characteristic

110

C₈

C₄⋊Dic₇₃

yes

characteristic

111

C₂²

#14556511

yes

characteristic

112

C₂²

#14556512

yes

characteristic

113

C₂²

#14556524

yes

characteristic

114

C₂²

#14556532

yes

characteristic

115

C₂²

#14556534

yes

characteristic

116

C₂²

#14556535

yes

characteristic

117

C₂²

#14556537

yes

characteristic

118

C₄

—

119

C₄

—

584

—

120

C₄

#14556498

yes

characteristic

121

C₄

#14556514

yes

characteristic

122

C₄

#14556515

yes

characteristic

123

C₄

#14556522

yes

characteristic

124

C₂

#17988349

yes

characteristic

125

C₂

#17988387

yes

characteristic

126

C₂

#17988388

yes

characteristic

127

C₂

#17988390

yes

characteristic

128

C₂

#17988391

yes

characteristic

129

C₂

#17988412

yes

characteristic

130

C₂

#17988414

yes

characteristic

	subgroup	G/H
center	C₂³	#11924013
commutator	C₈×C₇₃	C₄²
Frattini	C₂²×C₈	C₂×D₇₃
Fitting	C₂×#107×C₇₃	C₂
socle	C₂³×C₇₃	D₈
hypercenter	C₂×#107	D₇₃
hypocenter	C₇₃	#1380
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#107

subgroup

G/H

center

C₂³

#11924013

commutator

C₈×C₇₃

C₄²

Frattini

C₂²×C₈

C₂×D₇₃

Fitting

C₂×#107×C₇₃

C₂

socle

C₂³×C₇₃

D₈

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#107

N	H ≅ G/N	type
7. C₂×#11924003	C₄	semidirect
9. #14556525	C₄	semidirect
13. #107×C₇₃	C₄	semidirect
66. C₇₃	#1380	semidirect
79. #107	Dic₇₃	semidirect

H ≅ G/N

type

7. C₂×#11924003

C₄

semidirect

9. #14556525

C₄

semidirect

13. #107×C₇₃

C₄

semidirect

66. C₇₃

#1380

semidirect

79. #107

Dic₇₃

semidirect

Subgroups — #22608022

Conjugacy classes of subgroups

Complements